2011, University lecture series, ISBN 0821853317, Volume 57., ix, 200

Book

2017, University Lecture Series, ISBN 147044187X, Volume 69, 151 pages

Book

2011, Student mathematical library, ISBN 0821853686, Volume 60., xiii, 314

Book

Mathematische Annalen, ISSN 0025-5831, 12/2018, Volume 372, Issue 3-4, pp. 1041 - 1080

Let X be a real algebraic subset of Rn. We investigate the theory of algebraically constructible functions on X and the description of the semi-algebraic...

MATHEMATICS | SETS | Algebraic Geometry | Mathematics

MATHEMATICS | SETS | Algebraic Geometry | Mathematics

Journal Article

2006, 2nd ed., Algorithms and Computation in Mathematics, ISBN 9783540330981, Volume 10, ix, 662

The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and...

Data processing | Algorithms | Geometry, Algebraic | Algebraic Geometry | Algebra | Symbolic and Algebraic Manipulation | Geometry, algebraic | Mathematics

Data processing | Algorithms | Geometry, Algebraic | Algebraic Geometry | Algebra | Symbolic and Algebraic Manipulation | Geometry, algebraic | Mathematics

Book

Journal of the Institute of Mathematics of Jussieu, ISSN 1474-7480, 06/2014, Volume 17, Issue 4, pp. 673 - 702

Let X be a smooth complex projective manifold of dimension n equipped with an ample line bundle L and a rank k holomorphic vector bundle E. We assume that 1 <=...

random polynomial | real projective manifold | ample line bundle | Betti numbers | SURGERY | NUMBER | METRICS | SECTIONS | COMPLEX-MANIFOLDS | CRITICAL-POINTS | SUPERSYMMETRIC VACUA | ASYMPTOTICS | LINE BUNDLES | ZEROS | Topological manifolds | Algebra | Integers | Bundling | Mathematical analysis | Topology | Vectors (mathematics) | Estimates | Manifolds (mathematics) | Loci | Mathematics - Algebraic Geometry | Algebraic Geometry | Mathematics

random polynomial | real projective manifold | ample line bundle | Betti numbers | SURGERY | NUMBER | METRICS | SECTIONS | COMPLEX-MANIFOLDS | CRITICAL-POINTS | SUPERSYMMETRIC VACUA | ASYMPTOTICS | LINE BUNDLES | ZEROS | Topological manifolds | Algebra | Integers | Bundling | Mathematical analysis | Topology | Vectors (mathematics) | Estimates | Manifolds (mathematics) | Loci | Mathematics - Algebraic Geometry | Algebraic Geometry | Mathematics

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 01/2017, Volume 293, pp. 226 - 243

The solution set of a system of polynomial equations, called an algebraic set, can be decomposed into finitely many irreducible components. In numerical...

Intersection | Witness set | Regeneration | Algebraic set | Numerical algebraic geometry | MATHEMATICS, APPLIED | SOLUTION SETS | DECOMPOSITION | REAL POINTS | COMPUTING SINGULAR SOLUTIONS | HOMOTOPY | SOLVING POLYNOMIAL SYSTEMS | Algorithms

Intersection | Witness set | Regeneration | Algebraic set | Numerical algebraic geometry | MATHEMATICS, APPLIED | SOLUTION SETS | DECOMPOSITION | REAL POINTS | COMPUTING SINGULAR SOLUTIONS | HOMOTOPY | SOLVING POLYNOMIAL SYSTEMS | Algorithms

Journal Article

Mathematische Semesterberichte, ISSN 0720-728X, 3/2019, Volume 66, Issue 1, pp. 73 - 87

We give a new method relying on Coxeter chambers for the geometrical description of real algebraic varieties invariant under the $$CB_{n}$$ CB n -Coxeter...

Secondary: 14J70 | 14L24 | Mathematics | Invariant theory | 15A03 | 14J10 | 15A18 | Primary: 14R20 | Mathematics, general | Mirrors | Coxeter group | Real algebraic varieties | Chambers

Secondary: 14J70 | 14L24 | Mathematics | Invariant theory | 15A03 | 14J10 | 15A18 | Primary: 14R20 | Mathematics, general | Mirrors | Coxeter group | Real algebraic varieties | Chambers

Journal Article

2017, Volume 697

Order, lattices, ordered algebraic structures -- Ordered structures -- Ordered structures | Ordered algebraic structures | Integral transforms, operational calculus -- Integral transforms, operational calculus -- Moment problems | General topology -- Maps and general types of spaces defined by maps -- Real-valued functions | Number theory -- Forms and linear algebraic groups -- Forms and linear algebraic groups | Algebraic geometry -- Computational aspects in algebraic geometry -- Computational aspects in algebraic geometry | Several complex variables and analytic spaces -- Singularities -- Singularities | Model theory | Mathematical logic and foundations -- Model theory -- Model theory | Forms, Quadratic | Field theory and polynomials | Algebraic geometry -- Real algebraic and real analytic geometry -- Real algebraic and real analytic geometry | Semigroups | Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- Real-analytic and Nash manifolds | Geometry, Algebraic

Conference Proceeding

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 03/2018, Volume 113, Issue 13, pp. 1972 - 1994

Summary Domain decomposition strategies and proper generalized decomposition are efficiently combined to obtain a fast evaluation of the solution approximation...

parameterized solutions | reduced‐order models | proper generalized decomposition | domain decomposition | reduced-order models | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | APPROXIMATION | BASIS ELEMENT METHOD | SQUEEZE FLOWS | Jacobi matrix method | Domain decomposition methods | Jacobian matrix | Decomposition | Parameters | Approximation | 51 Geometry | Classificació AMS | Arithmetical algebraic geometry | Corbes | 14 Algebraic geometry | Equacions diferencials i integrals | Teoria de nombres | Geometria algèbrica | Àlgebra | Equacions diferencials el·líptiques | 11 Number theory | 11G Arithmetic algebraic geometry (Diophantine geometry) | Geometria algebraica | 35J Partial differential equations of elliptic type | Aritmètica | 35 Partial differential equations | Differential equations, Elliptic | Geometry | 14H Curves | Geometria | Matemàtiques i estadística | Equacions en derivades parcials | 51M Real and complex geometry | Àrees temàtiques de la UPC | Curves | Engineering Sciences

parameterized solutions | reduced‐order models | proper generalized decomposition | domain decomposition | reduced-order models | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | APPROXIMATION | BASIS ELEMENT METHOD | SQUEEZE FLOWS | Jacobi matrix method | Domain decomposition methods | Jacobian matrix | Decomposition | Parameters | Approximation | 51 Geometry | Classificació AMS | Arithmetical algebraic geometry | Corbes | 14 Algebraic geometry | Equacions diferencials i integrals | Teoria de nombres | Geometria algèbrica | Àlgebra | Equacions diferencials el·líptiques | 11 Number theory | 11G Arithmetic algebraic geometry (Diophantine geometry) | Geometria algebraica | 35J Partial differential equations of elliptic type | Aritmètica | 35 Partial differential equations | Differential equations, Elliptic | Geometry | 14H Curves | Geometria | Matemàtiques i estadística | Equacions en derivades parcials | 51M Real and complex geometry | Àrees temàtiques de la UPC | Curves | Engineering Sciences

Journal Article

Bulletin of Mathematical Biology, ISSN 0092-8240, 2/2019, Volume 81, Issue 2, pp. 337 - 360

Phylogenetic models admit polynomial parametrization maps in terms of the root distribution and transition probabilities along the edges of the phylogenetic...

Maximum likelihood estimation | Life Sciences, general | Mathematical and Computational Biology | Group-based models | Phylogenetics | Algebraic statistics | Mathematics | Real algebraic geometry | Cell Biology | Numerical algebraic geometry | DNA-SEQUENCES | INVARIANTS | ALGORITHM | PHYLOGENETIC TREES | EVOLUTIONARY TREES | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | Likelihood Functions | Markov Chains | Algorithms | Computational Biology | Mathematical Concepts | Models, Genetic | Models, Statistical | Phylogeny | Transition probabilities | Economic models | Group theory | Parameterization | Root distribution | Algebra | Maps | Models | Polynomials | Mathematical models | Maximum likelihood estimates | Algebraic Methods in Phylogenetics | Special Issue

Maximum likelihood estimation | Life Sciences, general | Mathematical and Computational Biology | Group-based models | Phylogenetics | Algebraic statistics | Mathematics | Real algebraic geometry | Cell Biology | Numerical algebraic geometry | DNA-SEQUENCES | INVARIANTS | ALGORITHM | PHYLOGENETIC TREES | EVOLUTIONARY TREES | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | Likelihood Functions | Markov Chains | Algorithms | Computational Biology | Mathematical Concepts | Models, Genetic | Models, Statistical | Phylogeny | Transition probabilities | Economic models | Group theory | Parameterization | Root distribution | Algebra | Maps | Models | Polynomials | Mathematical models | Maximum likelihood estimates | Algebraic Methods in Phylogenetics | Special Issue

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 07/2012, Volume 98, Issue 1, pp. 72 - 88

We prove the following CR version of Artinʼs approximation theorem for holomorphic mappings between real-algebraic sets in complex space. Let M⊂CN be a...

CR orbits | CR manifold | Algebraic map | MATHEMATICS | MATHEMATICS, APPLIED | SUBMANIFOLDS | REAL | HOLOMORPHIC MAPPINGS | Complex Variables | Algebraic Geometry | Mathematics

CR orbits | CR manifold | Algebraic map | MATHEMATICS | MATHEMATICS, APPLIED | SUBMANIFOLDS | REAL | HOLOMORPHIC MAPPINGS | Complex Variables | Algebraic Geometry | Mathematics

Journal Article

13.
Full Text
Numerical algebraic geometry for model selection and its application to the life sciences

Journal of the Royal Society Interface, ISSN 1742-5689, 10/2016, Volume 13, Issue 123, p. 20160256

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation and model selection. These...

Parameter estimation | Polynomial optimization | Maximum-likelihood | Model validation | Chemical reaction networks | POLYNOMIAL SYSTEMS | APOPTOSIS | PARAMETER-ESTIMATION | MULTIDISCIPLINARY SCIENCES | REAL POINTS | HOMOTOPY | model validation | chemical reaction networks | CONSTRUCTION | BIOLOGY | polynomial optimization | maximum-likelihood | parameter estimation | INVALIDATION | OPTIMIZATION | ERK | Models, Biological | 1004 | 181 | Life Sciences–Mathematics interface

Parameter estimation | Polynomial optimization | Maximum-likelihood | Model validation | Chemical reaction networks | POLYNOMIAL SYSTEMS | APOPTOSIS | PARAMETER-ESTIMATION | MULTIDISCIPLINARY SCIENCES | REAL POINTS | HOMOTOPY | model validation | chemical reaction networks | CONSTRUCTION | BIOLOGY | polynomial optimization | maximum-likelihood | parameter estimation | INVALIDATION | OPTIMIZATION | ERK | Models, Biological | 1004 | 181 | Life Sciences–Mathematics interface

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 11/2013, Volume 323, Issue 3, pp. 813 - 858

The purpose of this paper is to compute determinant index bundles of certain families of Real Dirac type operators on Klein surfaces as elements in the...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | INVARIANTS | ANALYTIC-TORSION | SPIN STRUCTURES | HOLOMORPHIC DETERMINANT BUNDLES | PHYSICS, MATHEMATICAL | CURVES | BOTT-CHERN FORMS | Algebraic Geometry | Mathematics | Differential Geometry | Algebraic Topology

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | INVARIANTS | ANALYTIC-TORSION | SPIN STRUCTURES | HOLOMORPHIC DETERMINANT BUNDLES | PHYSICS, MATHEMATICAL | CURVES | BOTT-CHERN FORMS | Algebraic Geometry | Mathematics | Differential Geometry | Algebraic Topology

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 6/2019, Volume 61, Issue 4, pp. 698 - 734

The 3SUM problem asks if an input n-set of real numbers contains a triple whose sum is zero. We qualify such a triple of degenerate because the probability of...

3SUM | 68Q25 | Computational Mathematics and Numerical Analysis | 68W40 | General position testing | 68R05 | Degeneracy testing | Mathematics | Range searching | Dominance reporting | Subquadratic algorithms | Combinatorics | Algebraic geometry | 68P10 | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Analysis | Algorithms | Computational geometry | Algebra | Real numbers | Upper bounds | Polynomials | Decision trees | Curves

3SUM | 68Q25 | Computational Mathematics and Numerical Analysis | 68W40 | General position testing | 68R05 | Degeneracy testing | Mathematics | Range searching | Dominance reporting | Subquadratic algorithms | Combinatorics | Algebraic geometry | 68P10 | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Analysis | Algorithms | Computational geometry | Algebra | Real numbers | Upper bounds | Polynomials | Decision trees | Curves

Journal Article

Revista Matemática Complutense, ISSN 1139-1138, 9/2018, Volume 31, Issue 3, pp. 545 - 593

We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies...

62J02 | Persistent homology | Mathematics | Real algebraic geometry | Topology | Point cloud data | Geometry | Interpolation | Algebra | Analysis | Mathematics, general | Applications of Mathematics | 13P25 | 14P25 | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Algebraic Geometry

62J02 | Persistent homology | Mathematics | Real algebraic geometry | Topology | Point cloud data | Geometry | Interpolation | Algebra | Analysis | Mathematics, general | Applications of Mathematics | 13P25 | 14P25 | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Algebraic Geometry

Journal Article

Foundations of Computational Mathematics, ISSN 1615-3375, 12/2012, Volume 12, Issue 6, pp. 805 - 849

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available...

60D05 | Semidefinite programming | Economics general | 52A41 | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Real algebraic geometry | 41A45 | Convex optimization | 90C25 | Numerical Analysis | 90C22 | Atomic norms | Math Applications in Computer Science | Applications of Mathematics | Computer Science, general | Gaussian width | Symmetry | MATHEMATICS, APPLIED | CUT | APPROXIMATION | ALGORITHM | EQUATIONS | RANK | SPACE | MATHEMATICS | RECOVERY | MINIMIZATION | NORM | COMPUTER SCIENCE, THEORY & METHODS | Geometry | Computational mathematics | Algebra | Optimization | Inverse problems | Mathematical analysis | Norms | Programming | Mathematical models | Matrices | Atomic structure | Matrix methods

60D05 | Semidefinite programming | Economics general | 52A41 | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Real algebraic geometry | 41A45 | Convex optimization | 90C25 | Numerical Analysis | 90C22 | Atomic norms | Math Applications in Computer Science | Applications of Mathematics | Computer Science, general | Gaussian width | Symmetry | MATHEMATICS, APPLIED | CUT | APPROXIMATION | ALGORITHM | EQUATIONS | RANK | SPACE | MATHEMATICS | RECOVERY | MINIMIZATION | NORM | COMPUTER SCIENCE, THEORY & METHODS | Geometry | Computational mathematics | Algebra | Optimization | Inverse problems | Mathematical analysis | Norms | Programming | Mathematical models | Matrices | Atomic structure | Matrix methods

Journal Article

Compositio Mathematica, ISSN 0010-437X, 1/2011, Volume 147, Issue 1, pp. 161 - 187

In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very...

real algebraic surfaces | very transitive actions | birational geometry | algebraic automorphisms | Cremona transformations | geometrically rational surfaces | rational surfaces | SINGULARITIES | FIELD | RESOLUTION | SUBGROUPS | CREMONA GROUP | biratonal geometry | MATHEMATICS | ALGEBRAIC VARIETY | PLANE | Geometry | Mathematical models | Conics | Algebra | Automorphisms | Bundles | Classification | Mathematics - Algebraic Geometry | Algebraic Geometry | Mathematics

real algebraic surfaces | very transitive actions | birational geometry | algebraic automorphisms | Cremona transformations | geometrically rational surfaces | rational surfaces | SINGULARITIES | FIELD | RESOLUTION | SUBGROUPS | CREMONA GROUP | biratonal geometry | MATHEMATICS | ALGEBRAIC VARIETY | PLANE | Geometry | Mathematical models | Conics | Algebra | Automorphisms | Bundles | Classification | Mathematics - Algebraic Geometry | Algebraic Geometry | Mathematics

Journal Article

Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 03/2014, Volume 2014, Issue 688, pp. 219 - 241

A classical result due to Segre states that on a real cubic surface in there exist two kinds of real lines: elliptic and hyperbolic lines. These two kinds of...

ENUMERATIVE GEOMETRY | MATHEMATICS | Geometric Topology | Algebraic Geometry | Mathematics

ENUMERATIVE GEOMETRY | MATHEMATICS | Geometric Topology | Algebraic Geometry | Mathematics

Journal Article

Annales Henri Poincare, ISSN 1424-0637, 07/2017, Volume 18, Issue 7, pp. 2251 - 2300

The notion of a topological phase of an insulator is based on the concept of homotopy between Hamiltonians. It therefore depends on the choice of a topological...

BUNDLES | SYMMETRIES | PHYSICS, MULTIDISCIPLINARY | NONCOMMUTATIVE GEOMETRY | QUANTUM-SYSTEMS | REAL | K-THEORY | CLASSIFICATION | PHYSICS, MATHEMATICAL | OPERATORS | PHYSICS, PARTICLES & FIELDS | Algebra

BUNDLES | SYMMETRIES | PHYSICS, MULTIDISCIPLINARY | NONCOMMUTATIVE GEOMETRY | QUANTUM-SYSTEMS | REAL | K-THEORY | CLASSIFICATION | PHYSICS, MATHEMATICAL | OPERATORS | PHYSICS, PARTICLES & FIELDS | Algebra

Journal Article